变形${\rm AdS}_5$模型中产生重夸克势和QCD β函数的对数修正
Logarithmic correction in the deformed ${\rm AdS}_5$ model to produce the heavy quark potential and QCD beta function
摘要：
我们研究了在变形的${\rm AdS}_5$翘曲因子中含有二次项$ -σz^2$和对数项$-c_0\log[(z_{IR}-z)/z_{IR}]$以及显式红外截止$z_{IR}$的\textit{holographic} QCD模型。本文研究了三种情况下的重夸克势，即只进行二次修正、同时进行二次和对数修正以及只进行对数修正。从爱因斯坦方程出发，求解了玻色子场和伸缩势，并在GKN框架下研究了相应的beta函数.我们的研究表明，在只有二次修正的情况下，负的$σ$或Andreev-Zakharov模型更适合于拟合重夸克势并产生双圈水平的QCD β函数，而在红外区，重夸克势是无界的.对于正$σ$或软壁${\rm AdS}_5$模型的情况，一个有趣的观察是对应的β函数存在红外不动点。在只作对数修正的情况下，重夸克Cornell势可以很好地拟合，相应的β函数与QCD β函数在双圈水平上相当好地吻合，并且在红外区重夸克Cornell势是有界的.最后，我们提出了一个更紧凑的模型，该模型只对变形翘曲因子进行对数修正，自由参数更少。
英文摘要：
We stude the \textit{holographic} QCD model which contains a quadratic term $ -σz^2$ and a logarithmic term $-c_0\log[(z_{IR}-z)/z_{IR}]$ with an explicit infrared cut-off $z_{IR}$ in the deformed ${\rm AdS}_5$ warp factor. We investigate the heavy quark potential for three cases, i.e, with only quadratic correction, with both quadratic and logarithmic corrections and with only logarithmic correction. We solve the dilaton field and dilation potential from the Einstein equation, and investigate the corresponding beta function in the G{ü}rsoy -Kiritsis-Nitti (GKN) framework. Our studies show that in the case with only quadratic correction, a negative $σ$ or the Andreev-Zakharov model is favored to fit the heavy quark potential and to produce the QCD beta-function at 2-loop level, however, the dilaton potential is unbounded in infrared regime. One interesting observing for the case of positive $σ$, or the soft-wall ${\rm AdS}_5$ model is that the corresponding beta-function exists an infrared fixed point. In the case with only logarithmic correction, the heavy quark Cornell potential can be fitted very well, the corresponding beta-function agrees with the QCD beta-function at 2-loop level reasonably well, and the dilaton potential is bounded from below in infrared. At the end, we propose a more compact model which has only logarithmic correction in the deformed warp factor and has less free parameters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
